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from the season 3 FAQ, http://competitive.na.leagueoflegends.com/season-3-faq

Quote:

What happens if I stop playing ranked for a while?

After 28 days of inactivity in a particular ranked queue, a couple things will happen. First, you’ll be hidden from the standings in your League, and you may lose League Points depending on your current tier. Every seven days thereafter, you’ll lose League Points again until you play a match in that queue.

The number of League Points lost following each period of decay is as follows:

Diamond: 50
Platinum: 35
Gold: 25
Silver: 10
Bronze: 0

If you fall below zero League Points as a result of decay, you’ll be placed into the next lowest division. If you’re already in Division V of your league, you’ll fall into a new league in the next tier down. This is currently the only way to get demoted to a lower tier.